i use the following code for count the authors

    $count_posts = wp_count_posts( 'download' );
    echo 'Published eBook (' . $count_posts->publish .  ')';
    echo ' ';
    global $wpdb; 
    $user_count = $wpdb->get_var( "SELECT COUNT(*) FROM $wpdb->users;" );
    echo '  Published Authors (' . $user_count . ')';

i need a count from authors who have the role frontend vendor or
who have published a downlaod post.

any idea?
thanks for help